This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: In the triangle pictured above show that \left(\frac{|AB|}{|AC|}\right)^2 + \left(\frac{|BC|}{|AC|}\right)^2 = 1 Deduce that $\sin^2{\theta} + \cos^2{\...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of a right triangle with $a$ the measure of angle $A$: Joyce knows that the sine of $a$ is the length of the side opposite $A$ divid...

This problem uses the same numbers and asks essentially the same mathematical questions as "6.NS Bake Sale," but that task requires students to apply the concepts of factors and common factors in a context.

Students have the opportunity to create and interpret data from simple daily questions.

This task provides students the opportunity to make use of units to find the gas need (N-Q.1). The key point is for them to explain their choices. This task provides an opportunity for students to practice MP2, Reason abstractly and quantitatively, and MP3, Construct viable arguments and critique the reasoning of others.

This task allows students to relate addition and subtraction problems to money in a context that introduces the concept of scarcity.

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

The purpose of this task is to have students work on a sequence of area problems that shows the advantage of increasingly abstract strategies in preparation for developing general area formulas for parallelograms and triangles.

This task asks students to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution, not just the least common denominator.

This task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator.

In this task students have the opportunity to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This real world problem is appropriate for mental mathematics and students should be encouraged to think through the solution mentally.

The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90_ and that angle measure is additive.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

This task helps students solidify their understanding of linear functions and push them to be more fluent in their reasoning about slope and y-intercepts. This task has also produced a reasonable starting place for discussing point-slope form of a linear equation.

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.